# [SCI] Machine Learning Theory

**Machine Learning Theory** is the mathematical study of algorithms that learn from data, including statistical learning theory, neural network expressibility, and generalisation bounds.

## Overview

Frank Rosenblatt's perceptron (1957) was the first trainable neural network. Minsky & Papert (1969) showed its limitations, causing the first "AI winter." Backpropagation (Rumelhart, Hinton, Williams, 1986) enabled multilayer networks. Vladimir Vapnik's Support Vector Machine and VC theory (1963–1995) provided statistical learning theory foundations. Yann LeCun's convolutional network for handwriting recognition (1989) proved deep networks could work. Statistical mechanics provided key insights: spin-glass models of neural networks (Hopfield 1982, Amit-Gutfreund-Sompolinsky 1985).

## Key Figures & Recognition

- **Geoffrey Hinton** (1947–), **Yann LeCun** (1960–), **Yoshua Bengio** (1964–): **Turing Award 2018**. Hinton: **Nobel Prize in Physics 2024** (shared with Hopfield).
- **John Hopfield** (1933–): Hopfield network, energy-based models. **Nobel Prize in Physics 2024**.
- **Vladimir Vapnik** (1936–): SVM, VC theory. No Nobel.

## Seminal Papers

- Rumelhart, D., Hinton, G. & Williams, R. ["Learning representations by back-propagating errors." *Nature* 323 (1986)](https://doi.org/10.1038/323533a0)
- [LeCun, Y. et al. "Gradient-Based Learning Applied to Document Recognition." *Proc. IEEE* 86 (1998)](https://doi.org/10.1109/5.726791)
- Hopfield, J. "Neural networks and physical systems with emergent collective computational abilities." *PNAS* 79 (1982).

## What This Enables
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- **[SCI] Deep Learning** — Deep learning is ML theory at scale: backpropagation, universal approximation, and optimisation theory all carry through.
- **[SCI] Genomics & Computational Biology** — Hidden Markov models, clustering, and neural networks trained on genomic data are ML applications.
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# Parents

* [SCI] Information Theory
* [SCI] Information Theory
* [SCI] Nonlinear Dynamics & Chaos Theory
* [TECH] Digital Computing